Active vibration isolation and sound isolation systems are known in the art. These systems utilize microprocessors (processors) to control or minimize mechanical vibration or ambient noise levels at a defined location or locations. Typical examples include noise or vibration experienced in an aircraft cabin or within an automobile passenger compartment. Generally, these active systems are responsive to at least one external input signal such as a synchronizing tachometer signal and/or error signal as supplied by various types of sensors such as microphones, accelerometers, etc. Generally, these systems strive to reduce to zero or at least minimize the recurring sound and/or vibration.
Examples of such systems are taught in U.S. Pat. No. 4,677,676 to Eriksson, U.S. Pat. No. 4,153,815 to Chaplin et al., U.S. Pat. No. 4,122,303 to Chaplin et al., U.S. Pat. No. 4,417,098 to Chaplin et al., U.S. Pat. No. 4,232,381 to Rennick et al., U.S. Pat. No. 4,083,433 to Geohegan, Jr. et al., U.S. Pat. No. 4,878,188 to Ziegler, Jr., U.S. Pat. No. 4,562,589 to Warnaka et al., U.S. Pat. No. 4,473,906 to Warnaka et al., U.S. Pat. No. 5,170,433 to Elliott et al., U.S. Pat. No. 4,689,821 to Salikuddin et al., U.S. Pat. No. 5,174,552 to Hodgson, and U.S. Pat. No. 5,133,527 to Chen et al., the disclosures of each are hereby incorporated by reference herein. In these types of systems, the algorithm used for control can be least mean square (LMS), Filtered-x LMS, or the like.
In active control systems of the above-mentioned type, it is generally required to have an input signal(s) which is supplied to an adaptive filter and/or a processor which is indicative of the frequency content and/or amplitude/phase of the input source, i.e., indicative of what is causing the disturbance. Particularly, for tonal control systems it is usually required to have two or more analog or digital waveforms, such as a sine and cosine wave, that are synchronized with, i.e., at the same frequency as, the input source signal for providing the appropriate information to the processor and/or adaptive filter.
A block diagram of a typical active control system is detailed in FIG. 1. The active control system 20 is comprised of an input source sensor 22 from which is derived a signal indicative of the source of the disturbance to be canceled, whether that disturbance is a mechanical vibration, a rotating unbalance, a source of acoustic noise, or the like. The sensor signal is conditioned by conditioner 24, such as by bandpass filtering and amplifying such that a usable signal is achieved. Conditioning of the signal may not be required as dictated by the application. The resulting signal is passed into a waveform generator 25. The waveform generator 25 provides the appropriate synchronized waveforms to the processor 28 and the adaptive filter 26.
For tonal control or control of a single vibrational input, the waveform generator 25 generates at least two analog or digital waves, such as a sine and cosine wave, which are synchronized in frequency with the input signal. The output from the waveform generator 25 is generally input to an adaptive filter 26 and generally also fed to a processor 28 to trigger the processor to perform the appropriate calculations. The input to the filter 26 generally has the form: EQU x.sub.k =A sin (.omega.kT)+B Cos (.omega.kT)
where
x.sub.k =input signal PA1 T=Sample period PA1 A=Amplitude of the real portion PA1 B=Amplitude of the imaginary portion PA1 W.sub.k =adaptive filter weight PA1 e.sub.k =error signal PA1 X.sub.k =the input signal PA1 .mu.=the adaptation coefficient which regulates the speed and stability of adaptation PA1 X.sub.k.sup.T =transpose of the X.sub.k vector PA1 d.sub.k =desired disturbance PA1 e.sub.k =error signal PA1 R.sub.k =a filtered version of the input signal
The filter 26 output contains each of the sine and cosine components, adjusted in amplitude by the adaptive weights W.sub.k. In a single input-single output (SISO) system, there is a single input x.sub.k and weights W.sub.0 and W.sub.1 are used to adaptively update the adaptive filter 26 in response to the error and/or input signal. The error sensor 30 provides a signal to the conditioner 24' which is indicative of the residual disturbance, i.e., the residual noise or vibration at the location of interest.
After being conditioned, the signal is inputted to the processor 28 where various calculations take place. The calculations take place according to an algorithm in order to produce updated adaptation coefficient weights. These updates to the weights occur according to an LMS algorithm, Filtered-x LMS algorithm, or the like. The output from the filter 26 is again conditioned by conditioner 24" and inputted to output device 32 to produce a output disturbance y.sub.k at the location of interest. The magnitude of the output disturbance y.sub.k in the ideal case is sufficient to minimize the mean square error e.sub.k.sup.2 at the sensor location. In other words, ideally, the error will be driven to zero.
Multiple input-multiple output (MIMO) systems are also known which utilize multiple input sensors, output devices, and error sensors. One such system is described in U.S. Pat. No. 5,216,722 to Popovich, the disclosure of which is hereby incorporated by reference herein. MIMO systems function essentially in the same fashion as SISO systems, albeit they are more computationally intensive.
In classical least mean square (LMS) control as illustrated by the block diagram of FIG. 2, an error signal e.sub.k is generated as the difference between the desired d.sub.k and the actual filter output y.sub.k. In the ideal case, the error signal is zero and the filter output y.sub.k is equal and opposite to the desired d.sub.k, thus completely canceling the disturbance (the vibration or sound pressure) at the predetermined location of interest. In classical LMS control, the error(s) e.sub.k and the input(s) x.sub.k are used to adaptively update the weight vector W.sub.k in a Finite Impulse Response (FIR) Filter according to the LMS algorithm. The weights are updated according to the relationship: EQU W.sub.k+1 =W.sub.k -.mu.e.sub.k X.sub.k
where
The error is derived from the equation EQU e.sub.k =d.sub.k -y.sub.k
Therefore, the error becomes EQU e.sub.k =d.sub.k -X.sub.k.sup.T W.sub.k
where
In most practical instances, it is desired to minimize the mean squared error (MSE) signal, i.e., the average power of the error signal. Therefore, the performance function to be minimized becomes: EQU e.sub.k.sup.2 =(d.sub.k +X.sub.k.sup.T W).sup.2 =d.sub.k.sup.2 +W.sup.T X.sub.k X.sub.k.sup.T W-2d.sub.k X.sub.k.sup.T W
This equation results in a multi-dimensional plot or quadratic performance surface which generally has one or more minima, which will be illustrated later. The classical LMS algorithm is fully described by Bernard Widrow and Samuel D. Stearns, Adaptive Signal Processing, Prentice-Hall, 1985.
The Filtered-x algorithm is a modification of the basic feedforward LMS algorithm. This modification is required when dynamics exist between the adaptive filter output and the error sensor signals. The modification to the update equation includes an estimate of the plant transfer function P. This estimate of the plant P enables the appropriate approximation of the gradient of the performance or error surface.
The block diagram of FIG. 3 illustrates a typical Filtered-x LMS algorithm. The major difference, as compared to classical LMS, is inclusion of plant dynamics. The plant estimate P which is obtained through a system identification (ID) step, is obtained either at startup or in an on-line fashion. The update equation for Filtered-x is given by: EQU W.sub.k+1 =W.sub.k -.mu.e.sub.k R.sub.k
where
Typical implementations of the Filtered-x LMS algorithm design the adaptation coefficient .mu. to be stable in the worst case. This is achieved by choosing a fixed or constant value of .mu. which is typically very small. For a fixed value of .mu., and when the plant gain is very low, the adaptation rate will also be very slow, but still stable. When the plant gain is very low, the adaptation rate was also very slow, but still stable. When the plant gain is very high, such as at a resonance peak, the adaptation rate will be correspondingly high. FIG. 3A illustrates this phenomena. Typically, the adaptation coefficient .mu. is frequency insensitive, i.e., it is a constant of the proper magnitude that insures stability of convergence at the worst case condition.
This illustrates one of the shortcomings of classical LMS and Filtered-x LMS algorithms. The adaptation coefficient .mu. is frequency insensitive. Thus, the adaptation rate must vary as a function of the frequency of the input disturbance because the plant transfer function P varies as a function of frequency. As a result of this, optimum convergence can never be achieved in these systems. U.S. Pat. No. 4,931,977 to Klemes describes a method of adaptive filtering that allows convergence in a fixed, predetermined amount of time by a Newton-method descent method, the disclosure of which is hereby incorporated by reference. Other references describing various adaptation methods are U.S. Pat. No. 5,260,896 to Iwasaki, U.S. Pat. No. 5,243,624 to Paik et al., U.S. Pat. No. 5,136,531 to McCaslin, U.S. Pat. No. 5,124,626 to Thoen, U.S. Pat. No. 5,058,047 to Chung, U.S. Pat. No. 4,989,170 to Batruni et al., U.S. Pat. No. 4,939,685 to Feintuch, and U.S. Pat. No. 4,878,188 to Ziegler, Jr.
Furthermore, under certain conditions when utilizing LMS control, the output from the digital processor to the adaptive filter can exceed the saturation limits. For example, when large disturbances are encountered. Because the filters and processors are only capable of outputting signals within predetermined operating limits or voltages, this can result in a detrimental square wave or clipped form to the filter output. Furthermore, when the output device is an actuator, operating the output device in this region may cause the actuator to overheat. Therefore, a solution to the clipping and overheating problems is needed.
FIG. 3B illustrates a typical saturated tonal waveform output. The output waveform is clipped, having a shape which approximates a square wave. Inputting this waveform into the actuator/output device can result in excitation of resonances or harmonics in the dynamic system. This is because the shape of the waveform will act as an impulsive input to the system, i.e., very similar to a hammer strike input which has a tendency to excite many resonant frequencies or modes. Furthermore, simply operating the output device in its nonlinear region may excite multiple harmonics. U.S. Pat. No. 4,736,460 to Rilling, U.S. Pat. No. 5,259,033 to Goodings et al., U.S. Pat. No. 5,216,692 to Ling, U.S. Pat. No. 4,268,829 to Baurle et al. all describe various methods of controlling signal amplitude and signal power levels.
Another problem with these active control systems utilizing LMS control is that the performance surface can contain singularities. Singularities can create serious performance problems when adaptive feedforward algorithms such as Filteredox LMS are used in MIMO systems. It is generally assumed that the quadratic performance surface, upon which the gradient based algorithms are based, has a global minimum. However, when there is no one local minima on the performance surface, a singularity exists.
FIG. 4A illustrates such a situation where there are multiple local minima or a trough in the quadratic performance surface. FIG. 4B illustrates a typical system with only one minima. When there is a global minima, the control system will be easily converged to minimize the mean square error (MSE) using LMS, Filtered-x LMS, or the like. However, where there is no one unique minima, but several minima, or a trough as shown in FIG. 4A, the system output may become saturated. Because of inaccuracies in the plant estimates which affect the gradient estimate, as well as certain kinds of noise, the output device signals u.sub.k may drift toward the saturation limits when a singularity condition is encountered. Therefore, this situation will impart unwanted harmonics into the system. These harmonics are caused by signal clipping and from operating within the nonlinear working region of the output device. Therefore, there is a need for a method of compensating for singularity conditions. One method of preventing overdrive of a transducer is provided in U.S. Pat. No. 5,278,913 to Delfosse et al.